This thread is already in development here:
http://forums.cgsociety.org/showthread.php?p=6278949#post6278949
Some very interesting ideas are been developed.
I decided to share this as an educational resource for some future students of fluid simulations like me. Theres a lot of information out there but not very organized.

There are several competing techniques for liquid simulation with a variety of trade-offs. The most common are Eulerian grid-based methods, smoothed particle hydrodynamics methods, vorticity-based methods, and Lattice Boltzmann methods. These methods originated in the computational fluid dynamics community, and have steadily been adopted by graphics practitioners over the past decade.

In computer graphics, the earliest attempts to solve the Navier-Stokes equations in full 3D came in 1996, by Nick Foster and Dimitris Metaxas. In 1999, Jos Stam published the so-called Stable Fluids method at SIGGRAPH, which exploited a semi-Lagrangian advection technique to provide unconditionally stable behaviour. This allowed for much larger time steps and in general, faster simulations. Blender 3d, uses a stable Lattice Boltzmann method implemented.

Maya uses which method exactly? I know the bases is Navier Stokes. In the market we have these softwares: FlowLine VFX, 3D Aliens, SitniSati, Katachi, Real Flow, Houdini, ILM Zeno and Softimage ICE.

Can someone tell me something about these too? what system is behind Realflow. Is it Eulerian? My doubt is here? does it uses a solver like Maya?
Cheers

Maya's fluids seems to be a primary implementation of the paper of Jos Stam (along with dozens of additional stuff of course). Realflow is a SPH simulator. Houdini has two (three actually) solvers: Level set (NS/Eulerian), fluid particles ( SPH) , and additionally semi Eulerian/Lagrangian solver (Sand Solver), which is kind of partly implemented. These are of course rough assumptions based on what you see outside. I've never touched Fumefx, but I bet it's a NS/Eulerian solver judging from a results.

ps Softimage ICE is not a solver, but architecture and environment, there are some solvers avaiable for it, but its design varies (I saw sph one).

RealFlow is not a fluid system. it's a particle and a rigid bodies system, it generates huge number of particles, and then it generate a mesh from those particles. they call it fluid simulator because it is use for water simulation mainly.

Softimage ICE is a rules base dynamics system , it blend particle, rigid and soft bodies in one node base interface. but again there are no navier stokes fluids.

Maya Fluids + Houdini Pyro + FumeFx are real fluid simulator they all work the same way by resolving a simplify navier-stokes equation in each voxel of the simulation.

my favorite is FumeFx because i find it better for transition beetween different state (fire -> smoke ).
Maya Fluids is Old but very strong great for smoke and fire. But when you need a transition fire to smoke i find Fume better.

i'm not good in houdini but i find Pyro very slow to render.

Fume and Pyro manage wavelet Turbulence , maya fluids don't.

for zeno and flowline i don't know but i guess they are both base on navier-stokes ...
i'm pretty sure that big part of the simulator in zeno workflow was coded with the help of ron fedkiw or some of his PHd Student. so all the best ... in one piece of software ...

So Navier-Stokes is the definitive algorithm for fluid dynamics based on newtonian laws and some assumptions and then Eulerian/Lagrangian are ways to solve the Navier-Stokes algorithm but also make assumptions as to be more computationally viable by effectively making it more simple, trading accuracy for speed?

If this is the case, would newtons 2nd law be the most accurate for solving fluid if computational speed was not an issue?